Two-wire full duplex digital transmission may be realized in many ways. Among them, echo-cancellation based transmission may achieve the best bandwidth efficiency, lowest transmission rate, and hence the longest range. A high echo cancellation level may be required to protect the far-end signal from the interference of the echo signal. In practice, in addition to 10–20 dB attenuation provided by an analog hybrid circuit, an extra compensation circuit may be required to reduce the echoes to an acceptable level. Usually, this is done by an echo canceller with digital implementation. A digital echo canceller uses data from the transmitter to reproduce the echo by modeling the echo path. Then, the replica of the echo may be subtracted from the received signal in the receiver section, as shown in FIG. 1. In digital subscriber line (DSL) transmission, for example, a practical communication system may require the echo canceller to achieve 60–70 dB echo cancellation.
An implementation of echo cancellation is the transversal filter structure. Given a hybrid circuit and a loop, the complexity of the echo canceller is determined by the factor of m/T. T denotes the symbol period, and m is the number of samples per baud depending on the subsequent processing of echo canceller. For example, most timing recovery techniques require at least two samples per baud (m=2) to retrieve the timing information from the received data signal. As a result, the echo canceller needs to be operated at twice the baud rate so as to provide echo-free samples to a timing recovery block and equalizer. Thus, the complexity of the echo canceller increases linearly with the sampling rate. For higher speed applications such as high bit rate digital subscriber line (HDSL), symmetric digital subscriber line (SDSL), and symmetric high bit rate digital subscriber line (SHDSL), hundreds of taps may be required to achieved the aforementioned high cancellation performance. Thus, there remains a need to efficiently provide echo cancellation.